B. Barış Alkan

Use of biplot technique for the comparison of the missing value imputation methods

This study was performed to assess the effects of different imputation methods on the performance of a biplot technique. We selected the Fishers iris data as our reference dataset. Some elements of the Iris data were deleted in different rates under missing at random MAR assumption to generate incomplete datasets which had 3.5%, 7%, 15%, 20% missing value. Datasets with missing values were completed by four imputation methods [mean imputation, regression imputation, expectation maximisation EM algorithm, multiple imputation MI]. The new imputed datasets were analysed by biplot technique and their results were compared with original complete biplot of the data. The results of biplot analysis were similar in all the imputation methods when missing rate is low under MAR assumption. Even when the missing rate was greater than 10%, results of EM and MI methods were similar to real values and graphical representation of original data. For multivariate methods, we also propose filling in the missing value with the arithmetic mean of the imputed estimates which are obtained with multiple imputation. This paper also indicates that the use of biplot technique for the comparison of the missing value imputation methods provides a useful visual tool.

A useful approach to identify the multicollinearity in the presence of outliers

The presence of outliers in the data sets affects the structure of multicollinearity which arises from a high degree of correlation between explanatory variables in a linear regression analysis. This affect could be seen as an increase or decrease in the diagnostics used to determine multicollinearity. Thus, the cases of outliers reduce the reliability of diagnostics such as variance inflation factors, condition numbers and variance decomposition proportions. In this study, we propose to use a robust estimation of the correlation matrix obtained by the minimum covariance determinant method to determine the diagnostics of multicollinearity in the presence of outliers. As a result, the present paper demonstrates that the diagnostics of multicollinearity obtained by the robust estimation of the correlation matrix are more reliable in the presence of outliers.

A comparison of different procedures for principal component analysis in the presence of outliers

Principal component analysis (PCA) is a popular technique that is useful for dimensionality reduction but it is affected by the presence of outliers. The outlier sensitivity of classical PCA (CPCA) has caused the development of new approaches. Effects of using estimates obtained by expectation–maximization – EM and multiple imputation – MI instead of outliers were examined on the artificial and a real data set. Furthermore, robust PCA based on minimum covariance determinant (MCD), PCA based on estimates obtained by EM instead of outliers and PCA based on estimates obtained by MI instead of outliers were compared with the results of CPCA. In this study, we tried to show the effects of using estimates obtained by MI and EM instead of outliers, depending on the ratio of outliers in data set. Finally, when the ratio of outliers exceeds 20%, we suggest the use of estimates obtained by MI and EM instead of outliers as an alternative approach.

Use of canonical variate analysis biplot in examination of choline content data of some foods

Adequate intake (AI) of choline as part of the daily diet can help prevent major diseases. Low choline intake is a major risk factor for liver and several neurological disorders. Extreme choline consumption may cause diseases such as hypotension, sweating, diarrhea, and fishy body odor. The AI of choline is 425 mg/day for adult women; higher for pregnant and lactating women. The AI for adult men is 550 mg/day. The total choline content of foods is calculated as the sum of free choline, glycerophosphocholine, phosphocholine, phosphatidylcholine and sphingomyelin. These are called the choline variables. Observed values of choline variables may be different in amounts of nutrients. So different food groups in terms of choline variables are useful to compare. The present paper shows the advantages of using canonical variate analysis biplot to optimally separate groups and explore the differentiality of choline variables amounts in foods.

Robust Principal Component Analysis based on Fuzzy Coded Data

In the presence of outlier s in the dataset, the principal component analysis method, like many of the classical statistical methods, is severely affected. For this reason, if there are outliers in dataset, researchers tend to use alternative methods. Use of fuzzy and robust approaches is the leading choice among these methods. In this study, a new approach to robust fuzzy principal component analysis is proposed. This approach combines the power of both robust and fuzzy methods at the same time and collects these two approaches under the framework of principal component analysis. The performance of proposed approach called robust principal component analysis based on fuzzy coded data is examined through a set of artificial dataset that are generated by considering three different scenarios and a real dataset to observe how it is affected by the increase in sample size and changes in the rate of outliers. In light of the studys findings, it is seen that the proposed approach gives better results than the ones in the classical and robust principal component analysis in the presence of outliers in dataset.

Comparison of Principal Component Analysis Biplots Based on Different Robust Covariance Matrix Estimates

Graphical approaches are widely used in the examination of multivariate data. The most popular of them is called Biplot. This technique provides an geometric approach that examined the relations between observations and variables in the principal components space with reduced-size. Principal component analysis (PCA) is obtained by covariance (or corelation) matrix. Therefore it is influenced by the presence of outliers. PCA biplot is used for visualization of PCA results. In this study, we compare the performances of PCA biplots based on different robust cavariance matrix estimates on the one real and the artificial data sets. Results indicate that Robust PCA biplot is preferred to instead of Classical PCA biplot in the presence of outliers.

Examination of relation between nutrient components and fruits: Biplot approach

Adequate intake of fruits and vegetables as part of the daily diet may help prevent major diseases. Low fruit intake is a major risk factor for cancer, coronary heart disease and stroke. The World Health Organization recommends eating at least five portions of a variety of fruit, which is nearly 400 g/day. Essential nutrients, water, carbohydrates, oils and vitamins are needed in appropriate quantities in order to have a well-functioning body. In this study we try to carry out a food composition study to identify and determine the chemical nature of the organic and inorganic macro-nutrient and micro-nutrient properties of the main fruit types that affect human nature, by a biplot graphical approach. The biplot can be considered as multivariate equivalents of scatter plots that have been used for graphically analyzing bivariate data. Biplot approaches show a simultaneous display of fruits and nutrient components in low dimensions. In the present study, the theory of biplot and different types of biplot will be given and than an application of the biplot approach will be applied to the real data.